Quality Loss Function Research Articles

Multi-objective genetic algorithm in reliability-based design optimization with sequential statistical modeling: an application to design of engine mounting

The present study explores reliability-based design optimization (RBDO) using multi-objective genetic algorithm (MOGA) in the context of practical engineering design. The reliability analysis is carried out using a most probable point-based method with first-order sensitivities. As an effective optimization approach, the two methods MOGA and RBDO are integrated to propose a multi-objective reliability-based design optimization (MORBDO). For considering the uncertainty propagation of reliable constraints, sequential statistical modeling is employed to estimate the appropriate distribution of probabilistic design variables. The present study also applies a multiresponse performance index based on the dimension reduction technique with a quality loss function. After verifying the MORBDO results using simulations on numerical problem, these techniques are applied to an automotive engine mounting system in the hierarchically decomposed problem of minimizing both the difference between the torque roll axis and the elastic roll axis and also the vibration transmissibility under mode purity and frequency requirements. The probabilistic design results indicate that the MORBDO results successfully identify more reliable and conservative optimized solutions than the deterministic results for a given reliability, and the failure probability is compared using a Monte Carlo simulation.

Economic manufacturing quantity model with machine breakdown and deteriorating production process

In this study, the author proposes a jointly setting model for determining the process mean and economic manufacturing quantity (EMQ) under the machine breakdown and deteriorating production process. The system addresses the corrective maintenance, preventive maintenance, and allowable shortage. The quality loss of conforming product is considered and Taguchi’s asymmetric quadratic quality loss function is used for evaluating the product quality. The optimal process mean and economic manufacturing quantity are jointly determined by minimizing the total expected cost of product per unit time including the set-up cost, holding cost, corrective maintenance cost, preventive maintenance cost, shortage cost. A solution procedure is devised to obtain the optimal solution and the sensitivity analysis of key parameters is conducted to investigate the effect on the optimal solution.

Integration of the variance of quadratic loss for evaluating process performance

This article interprets Taguchi’s quadratic quality loss function from a different viewpoint by considering the variance of quadratic loss as well as the mean of quadratic loss. The behavior of the variance of quadratic loss is characterized by the kurtosis and variance of the quality characteristic. To evaluate the location and dispersion performances of the quadratic loss simultaneously, a distance method linked with a Pareto front approach is proposed for process performance evaluation.

Optimization of Fractal Dimension of Turned AISI 1040 Steel Surface Considering Different Cutting Conditions

The present work examines the effect of turning process parameters, namely depth of cut and feed rate on the fractal dimension of AISI 1040 steel. Machined surfaces have been characterized using fractal dimensions. Apart from the aforesaid conventional turning parameters, cutting condition has been also considered as a design variable. Three cutting conditions have been considered, e.g. dry, water lubricated, and commercially available water-soluble emulsion lubricated condition. The depth of cut and feed rate has been also been varied at three levels. Experiments were performed following Taguchi's L9 orthogonal array. The optimal setting of process parameters has been achieved through the use of Taguchi's quality loss function represented by a signal-to-noise ratio. The optimal condition predicted from Taguchi's analysis is a 0.4 mm depth of cut, a 0.07 mm/rev feed rate and a water-based emulsion cutting environment. The results obtained for fractal dimensions has been also compared with the more conventional roughness parameter centre line average roughness which is dependent on instrument resolution.

Design of experiment based statistical approaches to optimize submerged arc welding process parameters

Joining of metals is very useful concept which is being utilized since Bronze Age and then gradual advancement gave rise to development of modern welding. And now welding is increasingly used in the fields of fabrication, manufacturing and construction. But productivity is the main concern in many manufacturing and industrial welding applications. Therefore selection of a welding process and its variables/parameters without sacrificing weld quality with respect to productivity and its quality is very important because an optimum blend of parameters which inevitably develop minimum or no defect will result in high productivity. For this study Submerge Arc Welding (SAW) process is selected for optimization because this versatile welding process is the first choice whenever good productivity with high quality requires in fabrication and manufacturing of Marine & pressure vessels, pipelines and offshore structures. Here Signal to noise (S/N) ratio analyses are used to find significant effects of key parameters on selected responses and then for optimization design of experiment based both quality loss function (OFM) and desirability function along with variance analyses by ANOVA are utilized. Moreover codes and standards provide a range for weld process parameters but author experienced that still there is a window to further optimize these parameters to produce the quality weld. Therefore this study is also useful to contribute in welding related research work by enhancing the knowledge of welding process and its analysis by utilizing advance statistical optimization techniques to find optimum zone within the acceptable zone from Code & Standard based tolerance Zone.

Economic statistical design of adaptive $$\bar{X}$$ control charts based on quality loss functions

An economic-statistical model is developed for variable parameters $$(VP){\bar{X}}$$ control chart is developed in which the constraints are imposed on the expected times to signal when the process is out of control and the expected number of false alarms per cycle. To improve chart effectiveness, the cost function is extended based upon the Taguchi philosophy of social loss of quality using the common loss functions including the linear, quadratic, exponential, and Linex. All of the loss functions that have been used up so far are symmetric, but what actually happens is that the imposed costs are not the same for over estimation and under estimation of the target value. For this reason, in this paper for the first time in the literature we use the Linex asymmetric loss functions, that results in the least average cost in all adaptive designs, compared to other symmetric loss functions. Using numerical example, we compare the performances of the $$VP{\bar{X}}$$ control charts with the others adaptive charts based on the loss function, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Results indicate a satisfactory performance for the proposed models.

A cubic quality loss function and its applications

AbstractThe traditional quality evaluation method believed that when the product quality characteristic was within the specification limit, no loss was produced. Taguchi proposed that even if the characteristic was within the range of users' demand, the fluctuation of quality characteristic would still cause loss to users and society. Therefore, he proposed a quadratic quality loss function to describe this loss. The function was established based on the Taylor expansion. It neglected terms with powers higher than 2, which would cause a certain deviation between the calculated and true value. Moreover, the tolerance and loss in the quadratic loss function must satisfied specific relationship, which limited its use. In this paper, the Taylor expansion items are raised to third order. The quality loss coefficients are discussed and analyzed so that the cubic quality loss function is established. In addition, the method of calculating hidden quality cost is given by using the cubic loss function. The hidden quality cost is affected by the quality loss coefficients and should be a range. The cubic quality loss function studies the inapplicability of quadratic loss function, so it widens the scope of application of quality loss function.

Economic parameter design for ultra-fast laser micro-drilling process

The basic requirement in this type of micro-drilling process is to achieve high product quality with the minimum machining cost, which can be realised through parameter design. In this paper, we propose a new economic parameter design under the framework of Bayesian modelling and optimisation. First of all, the Bayesian seemingly unrelated regression (SUR) models are utilised to develop the relationship models between input factors and output responses in the laser micro-drilling process. After that, simulated response values which reflect the real laser micro-drilling process are obtained by using the Gibbs sampling procedure. Moreover, a novel rejection cost function and a quality loss function are constructed based on the simulated responses. Finally, an optimisation scheme integrating the rejection cost (i.e. rework cost and scrap cost) function and the quality loss function is implemented by using multi-objective genetic algorithm to find feasible economic parameter settings for laser micro-drilling process.

Study and analysis on fuzzy quality control for the high-end manufacturing process based on Taguchi quality loss function

Study and analysis on fuzzy quality control for the high-end manufacturing process based on Taguchi quality loss function

A Design of Economic CUSUM Control Chart Incorporating Quality Loss Function

A Design of Economic CUSUM Control Chart Incorporating Quality Loss Function

Uji Kuat Tekan dan Daya Serap pada Batako dengan Menggunakan Metode Taguchi

The brick making process has two very critical characteristics / Critical To Quality (CTQ) , namely compressive strength and water absorption. For the quality characteristics of the compressive strength the greater the value, the better (Higher The Better). As for the absorption of water the quality characteristics are getting smaller, the better (Smaller The Better). The quality of the brick used as building material must have good quality that can maintain the strength of existing buildings. The quality in question is the compressive strength and absorbency of water produced must be in accordance with the requirements of SNI (Indonesian National Standard). The WS companies produce concrete blocks which have not good quality. The bricks are brittle. The method used in this study is the Taguchi method. Optimal Level Factor setting is Factor A (duration of stirring), Factor B (Pressure), Factor C (Water), Factor D (Drying) and Factor E (Composition of Sand and Lime). Where the optimal factor setting level factor that is most influential and dominant in compressive strength and water absorption is factor E (composition of sand and lime). For compressive strength factor E (sand and lime composition) level 2, 1: 0.25 and for absorption factor E (composition of sand and lime) level 1, 1: 0.5. and to confirm the results of this experimental design study, a percentage of Quality Loss Function of compressive strength and water absorption was obtained after the optimal level setting had a quality increase of 51.91% and a decrease in the Loss function of 78.5%.

A six sigma based approach to evaluate the on time performance of Indian railways

PurposeThe purpose of this paper is to propose an approach to evaluate “on time” performance for a class of Indian railways (IR). This approach is build-up on the theme of six sigma level computation for continues data. The arrival data obtained from a class of IR called “Rajdhani Express” exhibited a unique characteristic: neither did the data followed a distribution nor could it be transformed to fit into a distribution. In this work, the authors present an approach to evaluate on time performance of IR, given such “unruly” data.Design/methodology/approachAn attempt is made to develop a lucid approach, given an unruly data. Initially, the authors plot a histogram using Scott’s method. Later, the authors use Taguchi’s quality loss function to assign weights to each of the bins in histogram. Weights to each of the bins are assigned based on the predefined rules. Finally, sigma level is computed by using weighted defect per million opportunities (DPMO) approach. In this paper, the authors discuss the proposed algorithm, an illustrative example with an emphasis on a class of IR.FindingsGiven the unique characteristic (unruly data) of arrival data of IR, the proposed methodology helps in quantifying it is on time performance. This method extends the conventional DPMO approach of computing the sigma level. The proposed method is validated using various data sets of different distributions. Further, this approach can be generalized and applied to data set of any distribution. Since distribution of the data is not the pre-requisite, the proposed approach can be applied to compare (and benchmark) data sets of different distributions. This methodology, thus, paves path to develop newer approaches in quantifying and benchmarking the sigma levels.Research limitations/implicationsIn this manuscript, the authors present a case of Rajdhani Express trains, a class of IR. A practicing manager can use this approach to compare the performance of various classes of railways and benchmark their performance. Such an approach, with suitable modifications (if any) can be applied to evaluate performance in various service industries.Originality/valueUsually, if the data are unruly, the sigma level is computed by using ad-hoc methods that may provide compromising solutions and/or inaccurate results. The developed methodology proposes a unique approach to quantify sigma level, given such an unruly nature of the data. This approach thus fills the long needed gap in addressing such situations. This approach can be applied in various similar situations. A case of IR is presented.

Comprehensive identification of aircraft coordination feature based on complete importance modeling and its engineering application

PurposeCoordination feature (CF) is the information carrier in dimension and shape transfer process in aircraft manufacturing. The change of its geometric size, shape, position or other attributes would affect the consistency of accumulated errors between two or more assemblies. To identify these “key characteristics” that have a close relationship with the assembly precision, a comprehensive method was developed under digital manufacturing environment, which was based on importance calculation. The multi-hierarchy and multi-station assembly process of aircraft products were also taken into consideration.Design/methodology/approachFirst, the interaction and evaluation relationship between components at different manufacturing stages was decomposed with a hierarchical net. Second, to meet coordination accuracy requirements, with the integrated application of Taguchi quality loss function, accuracy principal and error correction coefficient H, the quality loss between target features and candidate features at adjacent assembly hierarchies were calculated, which was based on their precision variation. Third, the influence degree and affected degree of the features were calculated with DEMATEL (decision-making trial and evaluation laboratory) method, and the concepts of centrality degree index and cause degree index were proposed for calculating the complete importance degree to eventually identify the CFs.FindingsBased on the proposed methodology, CFs, affecting the skin profile and the flush coordination accuracy, were successfully identified at different assembly hierarchies to a certain type of wing flap component.Originality/valueBenefit results for the engineering application showed that the deviation of skin profile was more accurate than before, and the tolerance was also closer to the centerline of required assembly precision range. Moreover, the stability in the assembly process was increased by 26.9 per cent, which could bring a higher assembly quality and an enhancement on aircraft’s flight performance.

Artificial Neural Networks as a quality loss function for Six Sigma

In this study, Artificial Neural Networks (ANNs) are proposed to be used as a quality loss function for Six Sigma projects. An industrial data set consisting of power consumption rates of refrigerators and thermal camera readings around their compressors is analysed. For industrial data, relationships between inputs and outputs can be nonlinear and complex. Therefore, traditional statistical models may result in poor inferences. At this point, ANNs emerge as effective tools because of their ability to learn nonlinear and complex relationships. While Six Sigma remains as the major quality initiative, its popularity started to decline among industrial practitioners. Since the methodology was established, Six Sigma toolbox was not radically improved. Therefore, to enhance Six Sigma toolbox, an ANN-based structure is proposed to detect the refrigerators not complying with power specifications through thermal camera readings. Four quality loss function models are compared: one-dimensional parabolic Taguchi loss functions, multivariate Maximum Likelihood cost, logistic regression and finally ANNs. The analyses are conducted by Monte Carlo cross-validation to obtain precision-recall curves for these methods. The ANN-based cost function is shown to outperform other three methods. Finally, ANNs are found to be an effective tool which may bring new dimensions to Six Sigma concept.

Optimal manufacturing target setting by considering process adjustment cost and quality loss

In this study, the author considers the optimal manufacturing target setting problem with process adjustment cost and product quality loss. Assume that the process adjustment cost is proportional to the square of process mean and reciprocal of variance. The asymmetric linear quality loss function is adopted for measuring the product quality. The uniform distribution of quality characteristic is addressed in the formulation of mathematical model. The optimal manufacturing target will be obtained by minimizing the expected total cost of product.

The determination of product and process parameters under the non-normal distribution

Burr developed a density function that is able to represent a wide range of normal and non-normal distributions, and it has been shown that this density function can be easily applied to investigate the effect of non-normality in the studies of statistical process control (SPC). The process mean setting problem is one of the important topic for SPC. Traditionally, the product/process characteristic is assumed to be normally distributed. However, this assumption may not be true and there may exist non-normal characteristic in many practical production processes. In this paper, the work of process mean setting is examined by introducing Burr's density function as the underlying probability distribution of product/ process characteristic, such that the effect of non-normality to the determination of optimal process mean, standard deviation and specification limits of product/process characteristic can be studied. The linear asymmetrical quality loss function is addressed for measuring the quality loss of conforming product. The expected total cost of product includes the quality loss of conforming products, the rework cost of non-conforming product and the scrap cost of non-conforming product. A numerical example is provided for illustration.

Optimal process mean setting under the quality and cost

In this study, the author considers the optimal process mean setting problem with process adjustment cost and product quality. Assume that the process adjustment cost is proportional to the square of process mean and reciprocal of variance. Taguchi’s asymmetric quadratic quality loss function is adopted for measuring the product quality. The uniform and triangular distributions of quality characteristic are addressed in the formulation of mathematical model. The optimal process mean will be obtained by minimizing the expected total cost of product. Finally, the numerical example and sensitivity analysis of parameters are provided for illustration.

Methodological aspects of assessment and forecast of technical condion of the main installed equipment of power plants

The methodology is presented for assessment of the technical condition of an object, which is a separate unit of power equipment from a group of the same type of equipment of power plants. It is demonstrated that technical condition is a characteristic of quality of an object under investigation, which, for practical purposes, should be calculated as a deviation from an established value. The assessment of technical condition is fulfilled with uniform criteria based on a limited amount of initial data on each of the basic properties of the object. The assessment can be fulfilled at the level of the object performance indicator, at the level of the object individual property and at the level of a set of the object properties. The top level assessment is a function of the loss of quality by the object, which is calculated through convolution of low level values. The assessment of technical condition of an object is accompanied by calculation of uncertainty of quality loss functions by means of transformation of uncertainties of initial data into uncertainties of output values. The evaluation of the technical condition can be expressed either in relative units - the percentage of quality loss relative to the maximum possible quality of the object, or in absolute units - the monetary equivalent of a loss of quality by the object. Evaluation in relative units enables to determine the residual gamma resource of the object, but this requires the participation of an expert to assign the weight of performance indicators. Evaluation in absolute units makes it possible to identify objects whose improvement in technical condition is appropriate from the economic point of view. To track the reasons for deviations in the technical condition from the set values, a structured list of performance indicators and factors affecting them is used. It is shown that the possibilities of evaluating the technical condition in relative units are limited: an attempt to perform assessment and analysis of the technical condition by convolving values of indicators and characteristics of properties into a single numerical index gives incorrect results. Neglect of these restrictions leads to emergence of inadequate, unsubstantiated scientifically methodological requirements for assessment of the technical condition of power equipment.

Process Capability and Average Roughness in Abrasive Water Jet Cutting Process of Stainless Steel

Process capability analysis is frequently employed to evaluate if a product or a process can meet the customer’s requirement. In general, process capability analysis can be represented by using the process capability index. Until now, the process capability index was frequently used for manufacturing processes with quantitative characteristics. However, for a process with qualitative characteristic like cutting surface, the data’s type and single specification caused limitations of using the process capability index. Taguchi developed a surface quality by abrasive water jet cutting or quadratic quality loss function to address such issues. In this study, we intend to construct a measurable index which incorporates the process capability index philosophy concept to analyze the process capability with the consideration of the qualitative surface roughness. The manufacturers can employ the proposed index to self-assess the process capability. The objective of this study was to examine the effects of abrasive water jet machining variables like cutting speed of the stainless steel material. The roughness of the varied surface through the cut depth was also measured and determined as a process capability index of 3 zones machined surface.

Applying the Taguchi parametric design to optimize the solder paste printing process and the quality loss function to define the specifications

PurposeThis research aims to study the stencil printing process of the quad flat package (QFP) component with a pin pitch of 0.4 mm. After the optimization of the printing process, the desired inspection specification is determined to reduce the expected total process loss.Design/methodology/approachStatic Taguchi parametric design is applied while considering the noise factors possibly affecting the printing quality in the production environment. The Taguchi quality loss function model is then proposed to evaluate the two types of inspection strategies.FindingsThe optimal parameter-level treatment for the solder paste printing process includes a squeegee pressure of 11 kg, a stencil snap-off of 0.14 mm, a cleaning frequency of the stencil once per printing and using an air gun after stencil wiping. The optimal upper and lower specification limits are 119.8 µm and 110.3 µm, respectively.Originality/valueNoise factors in the production environment are considered to determine the optimal printing process. For specific components, the specification is established as a basis for subsequent processes or reworks.